Cakes cone in a variety of forms and flavours and are among favourite desserts served during special occasions such as birthday parties, Hari Raya, weddings and etc. Cakes are treasured not only because of their wonderful taste but also in the art of cake baking and cake decorating. Find out how, mathematics is used in cake baking and cake decorating and write about your findings.
Best Bakery shop received an order from your school to bake a 5 kg of round cake as shown in Diagram 1 for the Teachers' Day celebration.
1) If a kilogram of cake has a volume of 3800cm³, and the height of the cake is to be 7.0 cm, calculate the diameter of the baking tray to be used to fit the 5 kg cake ordered by your school. [Use π = 3.142]
2) The cake will be baked in an oven with inner dimensions of 80.0 cm in length, 60.0 cm in width and 45.0 cm in height.
a) If the volume of cake remains the same, explore by using different values of heights, h cm, and the corresponding values of diameters of the baking tray to be used, d cm. Tabulate your answers.
(b) Based on the values in your table,
(i) state the range of heights that is NOT sui table for the cakes and explain your answers.
(ii) suggest the dimensions that you think most suitable for the cake. Give reasons for your answer.
(c) (i) Form an equation to represent the linear relation between h and d. Hence, plot a suitable graph based on the equation that you have formed. [You may draw your graph with the aid of computer software.]
(ii) (a) If Best Bakery received an order to bake a cake where the height of the cake is 10.5 cm, use your graph to determine the diameter of the round cake pan required.
(b) If Best Bakery used a 42 cm diameter round cake tray, use your graph to estimate the height of the cake obtained.
3) Best Bakery has been requested to decorate the cake with fresh cream. The thickness of the cream is normally set to a uniform layer of about 1 cm.
(a) Estimate the amount of fresh cream required to decorate the cake using the dimensions that you have suggested in 2(b)(ii).
(b) Suggest thr ee of her shapes fo r cake , that will have t he same height and volume as those suggested in 2(b)(ii). Estimate the amount of fresh cream to be used on each of the cakes.
(c) Based on the values that you have found which shape requires the least amount of fresh cream to be used?
Find the dimension of a 5 kg round cake that requires the minimum amount of fresh cream to decorate. Use at least two different methods including Calculus.
State whether you would choose to bake a cake of such dimensions. Give reasons for your answers.
Best Bakery received an order to bake a multi-storey cake for Merdeka Day celebration, as shown in Diagram 2.
The height of each cake is 6.0 cm and the radius of the largest cake is 31.0 cm. The radius of the second cake is 10% less than the radius of the first cake, the radius of the third cake is 10% less than the radius of the second cake and so on.
(a) Find the volume of the first, the second, the third and the fourth cakes. By comparing all these values, determine whether the volumes of the cakes form a number pattern? Explain and elaborate on the number patterns.
(b) If the total mass of all the cakes should not exceed 15 kg, calculate the maximum number of cakes that the bakery needs to bake. Verify your answer using other methods.
While you were conducting the project, what have you learnt? What moral values did you practise? Represent your opinions or feelings creatively through usage of symbols, illustrations, drawing or even in a song.